The given name Randi originates from the Old Norse language, spoken by the medieval Scandinavian peoples. It is believed to have derived from the Old Norse word "randr," which means "shield bearer" or "warrior." This name was commonly used among the Viking communities that inhabited the coastal regions of modern-day Scandinavia, particularly in Norway and Iceland, during the 8th to 11th centuries.

In ancient Norse mythology, the name Randi is associated with the goddess Rind, who was known for her beauty and strength. She is mentioned in the Poetic Edda, a collection of Old Norse poems compiled in the 13th century, where she is described as one of the wives of the god Odin.

One of the earliest recorded instances of the name Randi can be found in the Icelandic Sagas, a series of literary works that document the lives and adventures of the Norse settlers in Iceland during the 9th to 11th centuries. The name appears in the Laxdæla Saga, written in the 13th century, where a character named Rannveig Randi is mentioned.

Throughout history, several notable figures have borne the name Randi. One of the most famous was Randi Haukdal (c. 1130-1200), a Norwegian chieftain and landowner who played a significant role in the Norwegian civil wars of the 12th century. Another prominent figure was Randi Thorleifsdottir (c. 1210-1280), an Icelandic chieftain and landowner who was known for her leadership and wisdom.

In the 17th century, Randi Edvardsdatter (1617-1690) was a Norwegian noblewoman and landowner who played a crucial role in the defense of her estates during the Kalmar War between Denmark and Sweden. Randi Jacobsdatter (1780-1868) was a Norwegian folk musician and singer, renowned for her preservation of traditional Norwegian folk songs and ballads.

In more recent times, Randi Weingarten (born 1957) is an American labor leader who has served as the president of the American Federation of Teachers since 2008. She has been a prominent advocate for teachers' rights and education reform in the United States.